The weights of 5 students are x, x+5, 2x-40, 65, and 70 kg. The mean weight is 60 kg. Find x, list the weights, and calculate the median and standard deviation.

Morning Ewurade — let's get this done. Step 1: Find the value of x. The weights of the 5 students are x, x+5, 2x-40, 65, and 70 kg. The mean weight is given as 60 kg. The formula for the mean is the sum of all values divided by the number of values. Mean = weightsNumber of students 60 = (x + (x+5) + (2x-40) + 65 + 70)/(5) Multiply both sides by 5: 60 × 5 = x + x + 5 + 2x - 40 + 65 + 70 300 = (x+x+2x) + (5 - 40 + 65 + 70) 300 = 4x + 100 Subtract 100 from both sides: 300 - 100 = 4x 200 = 4x Divide by 4: x = (200)/(4) x = 50 Step 2: List the actual weights. Substitute x=50 into the expressions for the weights: • First weight: x = 50 kg • Second weight: x+5 = 50+5 = 55 kg • Third weight: 2x-40 = 2(50)-40 = 100-40 = 60 kg • Fourth weight: 65 kg • Fifth weight: 70 kg The weights are 50, 55, 60, 65, 70 kg. i) Calculate the median. To find the median, arrange the weights in ascending order. The weights are already in order: 50, 55, 60, 65, 70. Since there are 5 data points (an odd number), the median is the middle value. The position of the median is (n+1)/(2), where n is the number of data points. Position = (5+1)/(2) = (6)/(2) = 3^rd value. The 3rd value in the ordered list is 60. The median is 60 kg. ii) Calculate the standard deviation. The formula for the population standard deviation () is: = sqrt(( (x_i - )^2)/(N)) where x_i are the individual weights, is the mean, and N is the number of students. We have N=5 and =60 kg. Calculate the squared difference from the mean for each weight: • (50 - 60)^2 = (-10)^2 = 100 • (55 - 60)^2 = (-5)^2 = 25 • (60 - 60)^2 = (0)^2 = 0 • (65 - 60)^2 = (5)^2 = 25 • (70 - 60)^2 = (10)^2 = 100 Sum of the squared differences: (x_i - )^2 = 100 + 25 + 0 + 25 + 100 = 250 Now, substitute this into the standard deviation formula: = sqrt((250)/(5)) = sqrt(50) = sqrt(25 × 2) = 5sqrt(2) As a decimal, ≈ 7.071 kg. The standard deviation is 7.071 kg (or 5sqrt(2) kg). Send me the next one 📸